This page addresses some of the basic principles that can be used to assess the accuracy of studies, and issues in the studies that should become apparent when these principles are violated.
BP vs. NBP (The Fatpad)
Within any study that measures both BP and NBP, the difference between the two forms for each length state (erect, stretch, flaccid) must equal the fadpad depth, and since the fatpad does not change depth appreciably for any of these states, the actual average BP-NBP difference is supposed to be approximately equivalent for each state.
This principle is well observed within indiviual studies, however, an issue arises across different studies because average fatpad depths vary between about 0.5"-1" due to different measuring tendencies and different populations having different degrees of body fat.
You'll notice that the BP/NBP differences for meta-studies tend to underestimate the separation, this is mainly due to potential for some studies having BP less than fully pressed and NBP partially pressed, and potential for misclassification of BP/NBP studies (BP/NBP ambiguity). These contribute biases for the NBP to be higher and the BP to be lower.
Stretched vs. Erect
The correlation is decent between the two, in theory the slope of their relationship depends on how much force is applied to stretch the penis, which would allow for the stretched average to be more or less than the erect average, but it's a safe assumption that the average stretched length will usually come out to less than the erect length on the order of tenths of an inch due to a tendency for under-stretching by researchers. This expectation can be used to cross validate results to find issues, such as finding the stretched length to be higher or significantly lower than the erect length. One example is that of Veale's results which give stretched greater than erect. When corrected as much as possible in the Veale+ average, this issue disappears and the erect becomes appreciably higher than the stretched in both BP and NBP methods (though Veale's limited number of studies measuring erect length still limits the erect results with a large margin of error).
I believe that one issue introducing further bias to under stretch the penis length comes from some studies pulling from behind the head, which results in a portion remaining unelongated, in my experience and in the studies it seems that the relationship between stretched and erect is much more consistent when measured by pulling with fingers on the head rather than behind it.
Self-reported vs. Researcher Measured
It goes without saying that researchers will tend to measure more reproducibly, whereas self-measurers will tend to over-measure themselves leading to unrealistic sizes being claimed and higher means, however there is another difference. Researchers usually try to standardize their method of measuring such that the same penis measured multiple times will reproducibly yield the same result. This allows for an estimate of the actual variability in the distribution of sizes in a population. However, when people measure themselves, standardization of these measurements is very limited such that a penis may measure a wide range of different sizes across different measurers. Self-measurement therefore introduces additional inter-measurer variability from people over-measuring and under-measuring in relation to each other. This usually leads to self-reported studies having much higher SDs than researcher measured studies. This doesn't mean that such wide variation exists in reality, but it does mean that such wide variation will tend to be found among the sizes people claim to have.
When sampling a clinical population there can be ample bias to underrepresent the SD. In fact there are almost only potential biases to reduce the SD, such that I currently expect the true variability to be poorly estimated by clinical studies, comparison to nearly random studies so far suggests this to be correct, maybe one day there will be enough compulsory randomly sampled studies to get more accurate results.